document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1157110>Question 1157110</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Anna can do a piece of work in 12 days. Beth can do the same work in 15 days. Charles can also do the same piece of work in 30 days. Anna starts the work and Beth joins her after 3 days. 3 days before the work is completed Anna leaves and Charles joins the work. In how many days will the work be completed? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #779918 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=779918\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You are given their rates of working:<BR>\n" );
document.write( "Anna: [ 1 job ] / [ 12 days ]<BR>\n" );
document.write( "Beth: [ 1 job ] / [ 15 days ]<BR>\n" );
document.write( "Charles [ 1 job ] / [ 30 days ]<BR>\n" );
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document.write( "Anna starts working alone and<BR>\n" );
document.write( "works for 3 days. In 3 days she<BR>\n" );
document.write( "does this fraction of the job:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+1%2F12+%29%2A3+=+1%2F4+ ALIGN=MIDDLE  ALT=\"+%28+1%2F12+%29%2A3+=+1%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "There is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%2F4+ ALIGN=MIDDLE  ALT=\"+3%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the job left<BR>\n" );
document.write( "-------------------------------------<BR>\n" );
document.write( "Anna and Beth then work together for<BR>\n" );
document.write( "an unknown number of days. <BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+ ALIGN=MIDDLE  ALT=\"+d+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the number of days they work together<BR>\n" );
document.write( "Their rate of working together is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F12+%2B+1%2F15+=+5%2F60+%2B+4%2F60+ ALIGN=MIDDLE  ALT=\"+1%2F12+%2B+1%2F15+=+5%2F60+%2B+4%2F60+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F12+%2B+1%2F15+=+9%2F60+ ALIGN=MIDDLE  ALT=\"+1%2F12+%2B+1%2F15+=+9%2F60+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9%2F60+=+3%2F20+ ALIGN=MIDDLE  ALT=\"+9%2F60+=+3%2F20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The fraction of the remaining work they get done is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+3%2F20+%29%2Ad%2A%283%2F4%29+=+%28+9%2F80+%29%2Ad+ ALIGN=MIDDLE  ALT=\"+%28+3%2F20+%29%2Ad%2A%283%2F4%29+=+%28+9%2F80+%29%2Ad+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So now <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F4+%2B+%28+9%2F80+%29%2Ad++ ALIGN=MIDDLE  ALT=\"+1%2F4+%2B+%28+9%2F80+%29%2Ad++\"   DISABLED_style= \"max-width:90%; height:auto;\" > is done<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+-+1%2F4+-+%28+9%2F80+%29%2Ad+=+3%2F4+-+%28+9%2F80+%29%2Ad+ ALIGN=MIDDLE  ALT=\"+1+-+1%2F4+-+%28+9%2F80+%29%2Ad+=+3%2F4+-+%28+9%2F80+%29%2Ad+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is<BR>\n" );
document.write( "the fraction left to do<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "Now for 3 days, Charles and Beth work together<BR>\n" );
document.write( "and they finish the job<BR>\n" );
document.write( "Add their rates of working<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F15+%2B+1%2F30+=+%28+3%2F4+-+%28+9%2F80+%29%2Ad+%29+%2F+3+ ALIGN=MIDDLE  ALT=\"+1%2F15+%2B+1%2F30+=+%28+3%2F4+-+%28+9%2F80+%29%2Ad+%29+%2F+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F15+%2B+1%2F30+=+1%2F4+-+%28+3d+%29+%2F+80+ ALIGN=MIDDLE  ALT=\"+1%2F15+%2B+1%2F30+=+1%2F4+-+%28+3d+%29+%2F+80+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2F30+%2B+1%2F30+=+20%2F80+-+%283d%29%2F80+ ALIGN=MIDDLE  ALT=\"+2%2F30+%2B+1%2F30+=+20%2F80+-+%283d%29%2F80+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3%2F30+=+%28+20+-+3d+%29+%2F+80+ ALIGN=MIDDLE  ALT=\"+3%2F30+=+%28+20+-+3d+%29+%2F+80+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%2F10+=+%28+20+-+3d+%29%2F+80+ ALIGN=MIDDLE  ALT=\"+1%2F10+=+%28+20+-+3d+%29%2F+80+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+80+ ALIGN=MIDDLE  ALT=\"+80+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8+=+20+-+3d+ ALIGN=MIDDLE  ALT=\"+8+=+20+-+3d+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3d+=+12+ ALIGN=MIDDLE  ALT=\"+3d+=+12+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+d+=+4+ ALIGN=MIDDLE  ALT=\"+d+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So Anna and Beth worked together for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4+ ALIGN=MIDDLE  ALT=\"+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > days<BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( "Add up the days they all worked:<BR>\n" );
document.write( "Anna alone: 3 days<BR>\n" );
document.write( "Anna & Beth: 4 days<BR>\n" );
document.write( "Charles and Beth: 3 days<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3+%2B+4+%2B+3+=+10+ ALIGN=MIDDLE  ALT=\"+3+%2B+4+%2B+3+=+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "They finish the work in 10 days<BR>\n" );
document.write( "------------------------------------<BR>\n" );
document.write( "Check my math and get a 2nd opinion if needed\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );